Geodesic
Subdirect products of certain varieties of unary algebras
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 2, pp. 573-578 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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J. Płonka in [12] noted that one could expect that the regularization ${\mathcal R}(K)$ of a variety ${K}$ of unary algebras is a subdirect product of ${K}$ and the variety ${D}$ of all discrete algebras (unary semilattices), but is not the case. The purpose of this note is to show that his expectation is fulfilled for those and only those irregular varieties ${K}$ which are contained in the generalized variety ${TDir}$ of the so-called trap-directable algebras.
J. Płonka in [12] noted that one could expect that the regularization ${\mathcal R}(K)$ of a variety ${K}$ of unary algebras is a subdirect product of ${K}$ and the variety ${D}$ of all discrete algebras (unary semilattices), but is not the case. The purpose of this note is to show that his expectation is fulfilled for those and only those irregular varieties ${K}$ which are contained in the generalized variety ${TDir}$ of the so-called trap-directable algebras.
Classification : 08A60, 08A70, 08B15, 08B26
Keywords: unary algebra; subdirect product; variety; directable algebra 
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     author = {\'Ciri\'c, M. and Petkovi\'c, T. and Bogdanovi\'c, S.},
     title = {Subdirect products of certain varieties of unary algebras},
     journal = {Czechoslovak Mathematical Journal},
     pages = {573--578},
     year = {2007},
     volume = {57},
     number = {2},
     mrnumber = {2337615},
     zbl = {1174.08301},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2007_57_2_a3/}
}
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Ćirić, M.; Petković, T.; Bogdanović, S. Subdirect products of certain varieties of unary algebras. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 2, pp. 573-578. http://geodesic.mathdoc.fr/item/CMJ_2007_57_2_a3/